English

Path regularity of coupled McKean-Vlasov FBSDEs

Probability 2020-11-16 v1

Abstract

This paper establishes H\"{o}lder time regularity of solutions to coupled McKean-Vlasov forward-backward stochastic differential equations (MV-FBSDEs). This is not only of fundamental mathematical interest, but also essential for their numerical approximations. We show that a solution triple to a MV-FBSDE with Lipschitz coefficients is 1/2-H\"{o}lder continuous in time in the LpL^p-norm provided that it admits a Lipschitz decoupling field. Special examples include decoupled MV-FBSDEs, coupled MV-FBSDEs with a small time horizon and coupled stochastic Pontryagin systems arsing from mean field control problems.

Keywords

Cite

@article{arxiv.2011.06664,
  title  = {Path regularity of coupled McKean-Vlasov FBSDEs},
  author = {Christoph Reisinger and Wolfgang Stockinger and Yufei Zhang},
  journal= {arXiv preprint arXiv:2011.06664},
  year   = {2020}
}

Comments

The results in this paper replace Sections 2 and 5 of arXiv:2009.08175v1